### Some articles on *turing degrees, turing, degrees*:

Recursion Theory - Areas of Research - Relative Computability and The

... on relative computability, a generalization of

**Turing Degrees**... on relative computability, a generalization of

**Turing**computability defined using oracle**Turing**machines, introduced by**Turing**(1939) ... An oracle**Turing**machine is a hypothetical device which, in addition to performing the actions of a regular**Turing**machine, is able to ask questions ... Informally, a set of natural numbers A is**Turing**reducible to a set B if there is an oracle machine that correctly tells whether numbers are in A when run with B as the oracle set (in this case, the set A is ...Theodore Slaman

... Hugh Woodin formulated the Bi-interpretability Conjecture for the

... Hugh Woodin formulated the Bi-interpretability Conjecture for the

**Turing degrees**, which conjectures that the partial order of the**Turing degrees**is ... Conjecture is equivalent to there being no nontrivial automorphism of the**Turing degrees**... They also exhibited limits on the possible automorphisms of the**Turing degrees**by showing that any automorphism will be arithmetically definable ...Recursion Theory - Areas of Research - Automorphism Problems

... of recursively enumerable sets, automorphisms are also studied for the structure of the

... of recursively enumerable sets, automorphisms are also studied for the structure of the

**Turing degrees**of all sets as well as for the structure of the**Turing degrees**of r.e ... both cases, Cooper claims to have constructed nontrivial automorphisms which map some**degrees**to other**degrees**this construction has, however, not been verified ...Structure of The

... A great deal of research has been conducted into the structure of the

**Turing Degrees**... A great deal of research has been conducted into the structure of the

**Turing degrees**... One general conclusion that can be drawn from the research is that the structure of the**Turing degrees**is extremely complicated ...### Famous quotes containing the word degrees:

“How have I been able to live so long outside Nature without identifying myself with it? Everything lives, moves, everything corresponds; the magnetic rays, emanating either from myself or from others, cross the limitless chain of created things unimpeded; it is a transparent network that covers the world, and its slender threads communicate themselves by *degrees* to the planets and stars. Captive now upon earth, I commune with the chorus of the stars who share in my joys and sorrows.”

—Gérard De Nerval (1808–1855)